I Can't Figure Out How to Build This Chair
For both the chassis and the slats he is just arraying a mesh along a curve, so he's mainly using 2 modifiers: Array and Curve. You'll easily find tutorials on this matter. For the slats, it gives that (I won't use a Mirror modifier but it doesn't make a big difference):

Create a bezier curve, give it the profile of the chair back along the X axis (it will make the array along curve easier to keep this axis)
Create a plane, stretch it in Edit mode on the Y axis. Make sure its origin is at the same place as the curve's origin:



Give the plane an Array modifier, choose the amount of instances (Count), enable Relative Offset and choose a X value of 1.2 for example, so that you keep a gap between the instances.
Give it a Curve modifier, choose the bezier curve as Object, choose X as Deformation Axis:




To change the slat length, select the bezier curve, go in Edit mode, select a vertex, and press AltS to scale:



You can create additional vertices for the curve: go in Edit mode and right click &gt; Subdivide. And you can give thickness to your plane with a Solidify modifier: